when is it necessary to have a continuous mesh over separate pieces?
To be clear: First you say 


  Everywhere I look people say that animated models need to be one continuous mesh with quads.


Then you say


  A lot of tutorials of people who are doing hard surface modeling via poly modeling vs sculpting often model there final object with several different pieces.


Simply understand that it's not necessarily a contradiction for people to be saying these two different things, because not all modeling projects have the same goal. I suspect that many of those you've been hearing are simply making assumptions about what other people are going to be doing with their models, and so maybe they are not entirely clear about their own goals when explaining their methods, so that others will understand what those methods are best suited to accomplish. Sometimes we take too much for granted.

Hard surface modeling can use various separated parts, just as you say--and even boolean them together without worry--because the end result will not need deformations. When you hear people say that models need to be one continuous mesh with quads, they are likely assuming the goal of organic modeling, such as for characters. 

Once this is understood, the course becomes rather clear, and there's no need for concern. For a helmet, you could probably do whatever you wanted. The only real issue I can foresee might arise from the fact that you want this model for 3D printing. That is going to require you to take more care than might otherwise be necessary, but I can't say in exactly what way, as I am not an expert on modeling for printing purposes. It might be a good idea to research this topic specifically, since the cost of physical material is at stake.